You can put in your own integration formula:
Unprotect[Integrate];
Integrate[x_ PolyLog[n_, Exp[x_]], x_] :=
x PolyLog[n + 1, Exp[x]] - x PolyLog[n + 2, Exp[x]]
Protect[Integrate];
Then
Integrate[(x + a) PolyLog[n, b Exp[c x]], x]
will integrate
Cheers,
Dave Snead
-----Original Message-----
From: Hui
Sent: Sunday, November 25, 2012 2:00 AM
To: mathgroup at smc.vnet.net
Subject: [mg128797] Manually tell Mathematica how to evaluate integrals
Hi all,
I have a question about Mathematica's abilities to solve integrals. There
seem to be cases where an antiderivative is explicitly known yet Mathematica
fails to compute the integral. One example of this would be
Integrate[x PolyLog[n,Exp[x]],x]
which Mathematica only solves for n=1,2, even though it is quite easy to
find a solution for higher values of n as well, namely
x PolyLog[n+1,Exp[x]] - x PolyLog[n+2,Exp[x].
I would like to know if it possible to teach Mathematica this integral in
such a way that it will also recognise and solve it in more complicated
cases such as
Integrate[(x+a) PolyLog[n,b Exp[c x]],x].
Thank you very much, your assistance is much appreciated!
Hui